The classes of moving averages and harmonizable processes are disjoint when the index of stability \(\alpha \)  is less then 2.
Only in the case \(\alpha =2\) , i.e. in the Gaussian case, one may find both a moving average representation and a harmonizable representation for the same process [1]}.
Between moving average and the harmonizable processes, the latter have attracted little attention from a statistical point of view so far.
This is mainly due to their non-ergodicity [2]}.
